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Journal Article

A variational principle for stationary, axisymmetric solutions of Einstein's equations

MPS-Authors

Dain,  Sergio
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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cqg6_23_016.pdf
(Publisher version), 189KB

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Citation

Dain, S. (2006). A variational principle for stationary, axisymmetric solutions of Einstein's equations. Classical and Quantum Gravity, 23(23), 6857-6871.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-4A4B-6
Abstract
Stationary, axisymmetric, vacuum, solutions of Einstein's equations are obtained as critical points of the total mass among all axisymmetric and (t, phi) symmetric initial data with fixed angular momentum. In this variational principle, the mass is written as a positive definite integral over a spacelike hypersurface. It is also proved that if an absolute minimum exists then it is equal to the absolute minimum of the mass among all maximal, axisymmetric, vacuum, initial data with fixed angular momentum. Arguments are given to support the conjecture that this minimum exists and is the extreme Kerr initial data.